There is a polygon of 2k sides. The following exercise is undertaken on the polygon:2 of its adjacent sides with the common vertex are removed and one side is added to join the vertices to complete the polygon. This is continued till the polygon with the least number of sides is formed.If the sum of the total number of diagonals of all polygons formed is 210 then kis:Correct answer is '6'. Can you explain this answer?

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There is a polygon of 2k sides. The following exercise is undertaken on the polygon:
2 of its adjacent sides with the common vertex are removed and one side is added to join the vertices to complete the polygon. This is continued till the polygon with the least number of sides is formed.
If the sum of the total number of diagonals of all polygons formed is 210 then k is:

Correct answer is '6'. Can you explain this answer?

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There is a polygon of 2k sides. The following exercise is undertaken o...

Here a new polygon with number of sides lesser than its parent polygon by 1 is formed after every exercise.
For any polygon the number of diagonals =

So the number of diagonals will be summation of the number of diagonals upto n = 4.

We see 2k = 12 satisfies the given equation.
Therefore, k = 6
Answer: 6

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There is a polygon of 2k sides. The following exercise is undertaken on the polygon:2 of its adjacent sides with the common vertex are removed and one side is added to join the vertices to complete the polygon. This is continued till the polygon with the least number of sides is formed.If the sum of the total number of diagonals of all polygons formed is 210 then kis:Correct answer is '6'. Can you explain this answer?

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